Distinguishing Primitive Permutation Groups

Abstract

Let $G$ be a permutation group acting on a set $V$. A partition $π$ of $V$ is distinguishing if the only element of $G$ that fixes each cell of $π$ is the identity. The distinguishing number of $G$ is the minimum number of cells in a distinguishing partition. We prove that if $G$ is a primitive permutation group and $|V|\ge336$, its distinguishing number is two.

A much stronger result was obtained earlier by Seress. His result is now cited. Since my methods might be of some interest, I have chosen to replace rather than withdraw the paper. It will not be submitted for publication